The surface height, or contour, of a three-dimensional (3-D) object can be determined quickly and easily by various non-contact optical methods such as moire topography, Fourier transform profilometry, spatial phase detection, and phase measuring profilometry (PMP). There are a wide range of practical applications to which these profilometric measurement methods can be directed, such as topographical mapping and measurement of the human body.
In a PMP system, light having a sinusoidal intensity distribution is projected onto a 3-D object to produce optical fringes. The pattern of fringes, as seen by a remotely positioned camera, can be represented mathematically as a function of the intensity distribution. By comparing the intensity distribution of the light patterns on the 3-D object, distorted by the contour of the object, with the intensity distribution of the same pattern of light projected onto a known reference plane, it is possible to compute, using basic geometry and multiple phase shifts, the surface height of each point on the 3-D object, relative to the reference plane. By computing the height of each point on the object, the surface contour of the object can be accurately measured.
The PMP method of surface height measurement works well for objects having generally continuous surfaces. However, when a pattern of light is projected onto an object having surface discontinuities, such as where one portion of the object overlaps another portion, several problems arise. First, some of the pixels of the captured image in these regions may not have reliable optical phase orders. Second, the phase order of neighboring pixels may vary by more than one. This is often referred to as "jump order."
Because of these problems, the measurement of surface contour in regions adjacent such a discontinuity is difficult using the PMP method, thus limiting the practical applications of the PMP method. For example, when a pattern of light is projected onto a human body that is turned at a slight angle from center, various discontinuities and shadowy regions appear in areas between the chest and arms, and between the legs. A camera typically is unable to distinguish the break point between an arm and the chest, based on the fringe pattern observed. As a result, the determination of surface contour at these locations is difficult, often times resulting in an incomplete measurement of the body contour.
Various solutions have been proposed to overcome the problems presented by surface discontinuities when performing surface contour measurement techniques. Reid et al. describe a modified version of Moire topography in which the contour interval has been greatly increased so that the entire depth of an object lies within one fringe. (See, G. T. Reid et al., Moire Topography With Large Contour Intervals, SPIE Vol. 814, Photomechanics and Speckle Metrology, p. 307-313, 1987). Unfortunately, this method is complicated and may not return highly accurate data around discontinuities.
Su et al. describe a method for phase-stepping grating profilometry of complex objects wherein both the discrete phase distribution and the modulation depth distribution are calculated. (See, X. Su et al., Phase-stepping Grating Profilometry: Utilization of Intensity Modulation Analysis in Complex Objects Evaluation, Optics Communications, Vol. 98, p. 141-150, 1993). Blocking lines are constructed by tracing down local minima in modulation depth function values and linking the pairs of poles having opposite signs. The blocking lines generally follow the lines of physical discontinuities. Unfortunately, these blocking lines may be difficult to generate automatically by a computer analyzing the digital image. This method also is complicated because the use of a mask may be required which may not return highly accurate data around discontinuities.